Showing papers on "Turbulence published in 2001"

The physical character of subaqueous sedimentary density flows and their deposits

Abstract: The complexity of flow and wide variety of depositional processes operating in subaqueous density flows, combined with post-depositional consolidation and soft-sediment deformation, often make it difficult to interpret the characteristics of the original flow from the sedimentary record. This has led to considerable confusion of nomenclature in the literature. This paper attempts to clarify this situation by presenting a simple classification of sedimentary density flows, based on physical flow properties and grain-support mechanisms, and briefly discusses the likely characteristics of the deposited sediments. Cohesive flows are commonly referred to as debris flows and mud flows and defined on the basis of sediment characteristics. The boundary between cohesive and non-cohesive density flows (frictional flows) is poorly constrained, but dimensionless numbers may be of use to define flow thresholds. Frictional flows include a continuous series from sediment slides to turbidity currents. Subdivision of these flows is made on the basis of the dominant particle-support mechanisms, which include matrix strength (in cohesive flows), buoyancy, pore pressure, grain-to-grain interaction (causing dispersive pressure), Reynolds stresses (turbulence) and bed support (particles moved on the stationary bed). The dominant particle-support mechanism depends upon flow conditions, particle concentration, grain-size distribution and particle type. In hyperconcentrated density flows, very high sediment concentrations (>25 volume%) make particle interactions of major importance. The difference between hyperconcentrated density flows and cohesive flows is that the former are friction dominated. With decreasing sediment concentration, vertical particle sorting can result from differential settling, and flows in which this can occur are termed concentrated density flows. The boundary between hyperconcentrated and concentrated density flows is defined by a change in particle behaviour, such that denser or larger grains are no longer fully supported by grain interaction, thus allowing coarse-grain tail (or dense-grain tail) normal grading. The concentration at which this change occurs depends on particle size, sorting, composition and relative density, so that a single threshold concentration cannot be defined. Concentrated density flows may be highly erosive and subsequently deposit complete or incomplete Lowe and Bouma sequences. Conversely, hydroplaning at the base of debris flows, and possibly also in some hyperconcentrated flows, may reduce the fluid drag, thus allowing high flow velocities while preventing large-scale erosion. Flows with concentrations <9% by volume are true turbidity flows (sensuBagnold, 1962), in which fluid turbulence is the main particle-support mechanism. Turbidity flows and concentrated density flows can be subdivided on the basis of flow duration into instantaneous surges, longer duration surge-like flows and quasi-steady currents. Flow duration is shown to control the nature of the resulting deposits. Surge-like turbidity currents tend to produce classical Bouma sequences, whose nature at any one site depends on factors such as flow size, sediment type and proximity to source. In contrast, quasi-steady turbidity currents, generated by hyperpycnal river effluent, can deposit coarsening-up units capped by fining-up units (because of waxing and waning conditions respectively) and may also include thick units of uniform character (resulting from prolonged periods of near-steady conditions). Any flow type may progressively change character along the transport path, with transformation primarily resulting from reductions in sediment concentration through progressive entrainment of surrounding fluid and/or sediment deposition. The rate of fluid entrainment, and consequently flow transformation, is dependent on factors including slope gradient, lateral confinement, bed roughness, flow thickness and water depth. Flows with high and low sediment concentrations may co-exist in one transport event because of downflow transformations, flow stratification or shear layer development of the mixing interface with the overlying water (mixing cloud formation). Deposits of an individual flow event at one site may therefore form from a succession of different flow types, and this introduces considerable complexity into classifying the flow event or component flow types from the deposits.

Particles and fields in fluid turbulence

Abstract: The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e., to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in nonequilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.

Density, velocity, and magnetic field structure in turbulent molecular cloud models

Abstract: We use three-dimensional (3D) numerical magnetohydrodynamic simulations to follow the evolution of cold, turbulent, gaseous systems with parameters chosen to represent conditions in giant molecular clouds (GMCs). We present results of three model cloud simulations in which the mean magnetic field strength is varied (B0 = 1.4-14 ?G for GMC parameters), but an identical initial turbulent velocity field is introduced. We describe the energy evolution, showing that (1) turbulence decays rapidly, with the turbulent energy reduced by a factor 2 after 0.4-0.8 flow crossing times (~2-4 Myr for GMC parameters), and (2) the magnetically supercritical cloud models gravitationally collapse after time ?6 Myr, while the magnetically subcritical cloud does not collapse. We compare density, velocity, and magnetic field structure in three sets of model snapshots with matched values of the Mach number ? 9,7,5. We show that the distributions of volume density and column density are both approximately log-normal, with mean mass-weighted volume density a factor 3-6 times the unperturbed value, but mean mass-weighted column density only a factor 1.1-1.4 times the unperturbed value. We introduce a spatial binning algorithm to investigate the dependence of kinetic quantities on spatial scale for regions of column density contrast (ROCs) on the plane of the sky. We show that the average velocity dispersion for the distribution of ROCs is only weakly correlated with scale, similar to mean size-line width distributions for clumps within GMCs. We find that ROCs are often superpositions of spatially unconnected regions that cannot easily be separated using velocity information; we argue that the same difficulty may affect observed GMC clumps. We suggest that it may be possible to deduce the mean 3D size-line width relation using the lower envelope of the 2D size-line width distribution. We analyze magnetic field structure and show that in the high-density regime n 103 cm-3, total magnetic field strengths increase with density with logarithmic slope ~1/3-2/3. We find that mean line-of-sight magnetic field strengths may vary widely across a projected cloud and are not positively correlated with column density. We compute simulated interstellar polarization maps at varying observer orientations and determine that the Chandrasekhar-Fermi formula multiplied by a factor ~0.5 yields a good estimate of the plane-of sky magnetic field strength, provided the dispersion in polarization angles is 25?.

Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows

Abstract: Particle image velocimetry (PIV) measurements are made in a highly turbulent swirling flow. In this flow, we observe a coexistence of turbulent fluctuations and an unsteady swirling motion. The proper orthogonal decomposition (POD) is used to separate these two contributions to the total energy. POD is combined with two new vortex identification functions, Γ1 and Γ2. These functions identify the locations of the centre and boundary of the vortex on the basis of the velocity field. The POD computed for the measured velocity fields shows that two spatial modes are responsible for most of the fluctuations observed in the vicinity of the location of the mean vortex centre. These two modes are also responsible for the large-scale coherence of the fluctuations. The POD computed from the Γ2 scalar field shows that the displacement and deformation of the large-scale vortex are correlated to these modes. We suggest the use of such a method to separate pseudo-fluctuations due to the unsteady nature of the large-scale vortices from fluctuations due to small-scale turbulence.

Simulations of Incompressible Magnetohydrodynamic Turbulence

Abstract: We simulate incompressible MHD turbulence using a pseudospectral code. Our major conclusions are: (1) MHD turbulence is most conveniently described in terms of counterpropagating shear Alfven and slow waves. Shear Alfven waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfven waves. Cascades composed entirely of shear Alfven waves do not generate a significant measure of slow waves. (2) MHD turbulence is anisotropic, with energy cascading more rapidly along k_⊥ than along k_∥, where k_⊥ and k_∥ refer to wavevector components perpendicular and parallel to the local magnetic field, respectively. Anisotropy increases with increasing k_⊥ such that excited modes are confined inside a cone bounded by k_∥ ∝ k^y_⊥, where γ 1. (4) MHD turbulence is generically strong in the sense that the waves that comprise it suffer order unity distortions on timescales comparable to their periods. Nevertheless, turbulent fluctuations are small deep inside the inertial range. Their energy density is less than that of the background field by a factor of Θ^((α-1)/(1-γ)) « 1. (5) MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines perturbed by counterpropagating waves. Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other. Shear Alfven waves are responsible for the mapping's shear and slow waves for its dilatation. The amplitude of the former exceeds that of the latter by 1/Θ(k_⊥), which accounts for dominance of the shear Alfven waves in controlling the cascade dynamics. (6) Passive scalars mixed by MHD turbulence adopt the same power spectrum as the velocity and magnetic field perturbations. (7) Decaying MHD turbulence is unstable to an increase of the imbalance between the fluxes of waves propagating in opposite directions along the magnetic field. Forced MHD turbulence displays order unity fluctuations with respect to the balanced state if excited at low k_⊥ by δ(t)-correlated forcing. It appears to be statistically stable to the unlimited growth of imbalance. (8) Gradients of the dynamic variables are focused into sheets aligned with the magnetic field whose thickness is comparable to the dissipation scale. Sheets formed by oppositely directed waves are uncorrelated. We suspect that these are vortex sheets, which the mean magnetic field prevents from rolling up. (9) Items 1-6 lend support to the model of strong MHD turbulence put forth by Goldreich & Sridhar (GS). Results from our simulations are also consistent with the GS prediction γ = 2/3, as are those obtained previously by Cho & Vishniac. The sole notable discrepancy is that one-dimensional energy spectra determined from our simulations exhibit α ≈ 3/2, whereas the GS model predicts α = 5/3. Further investigation is needed to resolve this issue.

Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9

Abstract: The mechanisms of sound generation in a Mach 0.9, Reynolds number 3600 turbulent jet are investigated by direct numerical simulation. Details of the numerical method are briefly outlined and results are validated against an experiment at the same flow conditions (Stromberg, McLaughlin & Troutt 1980). Lighthill's theory is used to define a nominal acoustic source in the jet, and a numerical solution of Lighthill's equation is compared to the simulation to verify the computational procedures. The acoustic source is Fourier transformed in the axial coordinate and time and then filtered in order to identify and separate components capable of radiating to the far field. This procedure indicates that the peak radiating component of the source is coincident with neither the peak of the full unfiltered source nor that of the turbulent kinetic energy. The phase velocities of significant components range from approximately 5% to 50% of the ambient sound speed which calls into question the commonly made assumption that the noise sources convect at a single velocity. Space–time correlations demonstrate that the sources are not acoustically compact in the streamwise direction and that the portion of the source that radiates at angles greater than 45° is stationary. Filtering non-radiating wavenumber components of the source at single frequencies reveals that a simple modulated wave forms for the source, as might be predicted by linear stability analysis. At small angles from the jet axis the noise from these modes is highly directional, better described by an exponential than a standard Doppler factor.

Fluid particle accelerations in fully developed turbulence

Abstract: The motion of fluid particles as they are pushed along erratic trajectories by fluctuating pressure gradients is fundamental to transport and mixing in turbulence. It is essential in cloud formation and atmospheric transport, processes in stirred chemical reactors and combustion systems, and in the industrial production of nanoparticles. The concept of particle trajectories has been used successfully to describe mixing and transport in turbulence, but issues of fundamental importance remain unresolved. One such issue is the Heisenberg-Yaglom prediction of fluid particle accelerations, based on the 1941 scaling theory of Kolmogorov. Here we report acceleration measurements using a detector adapted from high-energy physics to track particles in a laboratory water flow at Reynolds numbers up to 63,000. We find that, within experimental errors, Kolmogorov scaling of the acceleration variance is attained at high Reynolds numbers. Our data indicate that the acceleration is an extremely intermittent variable--particles are observed with accelerations of up to 1,500 times the acceleration of gravity (equivalent to 40 times the root mean square acceleration). We find that the acceleration data reflect the anisotropy of the large-scale flow at all Reynolds numbers studied.

Random Flow Generation Technique for Large Eddy Simulations and Particle-Dynamics Modeling

Abstract: A random flow generation (RFG) technique is presented, which can be used for initial/ inlet boundary generation in LES (Large-Eddy-Simulations) or particle tracking in LES/ RANS (Reynolds-Averaged Navier-Stokes) computations of turbulent flows. The technique is based on previous methods of synthesizing divergence-free vector fields from a sample of Fourier harmonics and allows to generate non-homogeneous anisotropic flow field representing turbulent velocity fluctuations. It was validated on the cases of boundary layer and flat plate flows. Applications of the technique to LES and particle tracking are considered

Statistical Theory and Modeling for Turbulent Flows

Abstract: Preface. Preface to second edition. Preface to first edition. Motivation. Epitome. Acknowledgements. Part I FUNDAMENTALS OF TURBULENCE. 1 Introduction. 1.1 The turbulence problem. 1.2 Closure modeling. 1.3 Categories of turbulent flow. Exercises. 2 Mathematical and statistical background. 2.1 Dimensional analysis. 2.1.1 Scales of turbulence. 2.2 Statistical tools. 2.2.1 Averages and probability density functions. 2.2.2 Correlations. 2.3 Cartesian tensors. 2.3.1 Isotropic tensors. 2.3.2 Tensor functions of tensors Cayley-Hamilton theorem. Exercises. 3 Reynolds averaged Navier-Stokes equations. 3.1 Background to the equations. 3.2 Reynolds averaged equations. 3.3 Terms of kinetic energy and Reynolds stress budgets. 3.4 Passive contaminant transport. Exercises. 4 Parallel and self-similar shear flows. 4.1 Plane channel flow. 4.1.1 Logarithmic layer. 4.1.2 Roughness. 4.2 Boundary layer. 4.2.1 Entrainment. 4.3 Free-shear layers. 4.3.1 Spreading rates. 4.3.2 Remarks on self-similar boundary layers. 4.4 Heat and mass transfer. 4.4.1 Parallel flow and boundary layers. 4.4.2 Dispersion from elevated sources. Exercises. 5 Vorticity and vortical structures. 5.1 Structures. 5.1.1 Free-shear layers. 5.1.2 Boundary layers. 5.1.3 Non-random vortices. 5.2 Vorticity and dissipation. 5.2.1 Vortex stretching and relative dispersion. 5.2.2 Mean-squared vorticity equation. Exercises. Part II SINGLE-POINT CLOSURE MODELING. 6 Models with scalar variables. 6.1 Boundary-layer methods. 6.1.1 Integral boundary-layer methods. 6.1.2 Mixing length model. 6.2 The k -epsilon model. 6.2.1 Analytical solutions to the k -epsilon model. 6.2.2 Boundary conditions and near-wall modifications. 6.2.3 Weak solution at edges of free-shear flow free-stream sensitivity. 6.3 The k -omega model. 6.4 Stagnation-point anomaly. 6.5 The question of transition. 6.5.1 Reliance on the turbulence model. 6.5.2 Intermittency equation. 6.5.3 Laminar fluctuations. 6.6 Eddy viscosity transport models. Exercises. 7 Models with tensor variables. 7.1 Second-moment transport. 7.1.1 A simple illustration. 7.1.2 Closing the Reynolds stress transport equation. 7.1.3 Models for the slow part. 7.1.4 Models for the rapid part. 7.2 Analytic solutions to SMC models. 7.2.1 Homogeneous shear flow. 7.2.2 Curved shear flow. 7.2.3 Algebraic stress approximation and nonlinear eddy viscosity. 7.3 Non-homogeneity. 7.3.1 Turbulent transport. 7.3.2 Near-wall modeling. 7.3.3 No-slip condition. 7.3.4 Nonlocal wall effects. 7.4 Reynolds averaged computation. 7.4.1 Numerical issues. 7.4.2 Examples of Reynolds averaged computation. Exercises. 8 Advanced topics. 8.1 Further modeling principles. 8.1.1 Galilean invariance and frame rotation. 8.1.2 Realizability. 8.2 Second-moment closure and Langevin equations. 8.3 Moving equilibrium solutions of SMC. 8.3.1 Criterion for steady mean flow. 8.3.2 Solution in two-dimensional mean flow. 8.3.3 Bifurcations. 8.4 Passive scalar flux modeling. 8.4.1 Scalar diffusivity models. 8.4.2 Tensor diffusivity models. 8.4.3 Scalar flux transport. 8.4.4 Scalar variance. 8.5 Active scalar flux modeling: effects of buoyancy. 8.5.1 Second-moment transport models. 8.5.2 Stratified shear flow. Exercises. Part III THEORY OF HOMOGENEOUS TURBULENCE. 9 Mathematical representations. 9.1 Fourier transforms. 9.2 Three-dimensional energy spectrum of homogeneous turbulence. 9.2.1 Spectrum tensor and velocity covariances. 9.2.2 Modeling the energy spectrum. Exercises. 10 Navier-Stokes equations in spectral space. 10.1 Convolution integrals as triad interaction. 10.2 Evolution of spectra. 10.2.1 Small-k behavior and energy decay. 10.2.2 Energy cascade. 10.2.3 Final period of decay. Exercises. 11 Rapid distortion theory. 11.1 Irrotational mean flow. 11.1.1 Cauchy form of vorticity equation. 11.1.2 Distortion of a Fourier mode. 11.1.3 Calculation of covariances. 11.2 General homogeneous distortions. 11.2.1 Homogeneous shear. 11.2.2 Turbulence near a wall. Exercises. Part IV TURBULENCE SIMULATION. 12 Eddy-resolving simulation. 12.1 Direct numerical simulation. 12.1.1 Grid requirements. 12.1.2 Numerical dissipation. 12.1.3 Energy-conserving schemes. 12.2 Illustrations. 12.3 Pseudo-spectral method. Exercises. 13 Simulation of large eddies. 13.1 Large eddy simulation. 13.1.1 Filtering. 13.1.2 Subgrid models. 13.2 Detached eddy simulation. Exercises. References. Index.

Computational Flow Modeling for Chemical Reactor Engineering

Abstract: Preface I Introduction 1 Reactor Engineering and Flow Modeling II Computational Flow Modeling 2 Mathematical Modeling of Flow Processes 3 Turbulent Flow Processes 4 Multiphase Flow Processes 5 Reactive Flow Processes 6 Numerical Solution of Model Equations 7 Numerical Solution of Complex Flow Models 8 Computational Tools for Simulating Flow Processes III CFM for CRE 9 Flow Modeling for Reactor Engineering IV Applications 10 Stirred Reactors 11 Bubble Column Reactors 12 Fluidized Bed Reactors 13 Fixed Bed and Other Types of Reactors V Epilogue 14 Epilogue

Simulations of bypass transition

Abstract: Bypass transition in an initially laminar boundary layer beneath free-stream turbulence is simulated numerically. New perspectives on this phenomenon are obtained from the numerical flow fields. Transition precursors consist of long backward jets contained in the fluctuating u-velocity field; they flow backwards relative to the local mean velocity. The jets extend into the upper portion of the boundary layer, where they interact with free-stream eddies. In some locations a free-stream perturbation to the jet shear layer develops into a patch of irregular motion – a sort of turbulent spot. The spot spreads longitudinally and laterally, and ultimately merges into the downstream turbulent boundary layer. Merging spots maintain the upstream edge of the turbulent region. The jets, themselves, are produced by low-frequency components of the free-stream turbulence that penetrate into the laminar boundary layer. Backward jets are a component of laminar region streaks.A method to construct turbulent inflow from Orr–Sommerfeld continuous modes is described. The free-stream turbulent intensity was chosen to correspond with the experiment by Roach & Brierly (1990). Ensemble-averaged numerical data are shown to be in good agreement with laboratory measurements.

Spatially Averaged Open-Channel Flow over Rough Bed

Abstract: In this paper it is suggested that the double-averaged (in temporal and in spatial domains) momentum equations should be used as a natural basis for the hydraulics of rough-bed open-channel flows, especially with small relative submergence. The relationships for the vertical distribution of the total stress for the simplest case of 2D, steady, uniform, spatially averaged flow over a rough bed with flat free surface are derived. These relationships explicitly include the form-induced stresses and form drag as components of the total stress. Using this approach, we define three types of rough-bed flows: (1) Flow with high relative submergence; (2) flow with small relative submergence; and (3) flow over a partially inundated rough bed. The relationships for the double-averaged velocity distribution and hydraulic resistance for all three flow types are derived and compared with measurements where possible. The double-averaged turbulent and form-induced intensities and stresses for the case of regular spherical-segment-type roughness show the dominant role of the double-averaged turbulence stresses and form drag in momentum transfer in the near-bed region.

Disturbance growth in boundary layers subjected to free-stream turbulence

Abstract: This paper aims at a description of boundary-layer flow which is subjected to free-stream turbulence in the range from 1–6% and is based on both flow visualization results and extensive hot-wire measurements. Such flows develop streamwise elongated regions of high and low streamwise velocity which seem to lead to secondary instability and breakdown to turbulence. The initial growth of the streaky structures is found to be closely related to algebraic or transient growth theory. The data have been used to determine streamwise and spanwise scales of the streaky structures. Both the flow visualization and the hot-wire measurements show that close to the leading edge the spanwise scale is large as compared to the boundary-layer thickness, but further downstream the spanwise scale approaches the boundary-layer thickness. Wavenumber spectra in both the streamwise and the spanwise directions were calculated. A scaling for the streamwise structure of the disturbance was found, which allows us to collapse the spectra from different downstream positions. The scaling combines the facts that the streaky structures increase their streamwise length in the downstream direction which becomes proportional to the boundary-layer thickness and that the energy growth is algebraic, close to proportional to the downstream distance.

Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst

Abstract: Two time-periodic solutions with genuine three-dimensional structure are numerically discovered for the incompressible Navier–Stokes equation of a constrained plane Couette flow. One solution with strong variation in spatial and temporal structure exhibits a full regeneration cycle, which consists of the formation and breakdown of streamwise vortices and low-velocity streaks; the other one, of gentle variation, represents a spanwise standing-wave motion of low-velocity streaks. These two solutions are unstable and the corresponding periodic orbits in the phase space are connected with each other. A turbulent state wanders around the strong one for most of the time except for occasional escapes from it. As a result, the mean velocity profile and the root-mean-squares of velocity fluctuations of the plane Couette turbulence agree very well with the temporal averages of those of this periodic motion. After an occasional escape from the strong solution, the turbulent state reaches the gentle periodic solution and returns. On the way back, it experiences an overshoot accompanied by strong turbulence activity like an intermittent bursting phenomenon.

Statistical evidence of hairpin vortex packets in wall turbulence

Abstract: The structure of velocity in the outer region of turbulent channel flow (y+ [gsim ] 100) is examined statistically to determine the average flow field associated with spanwise vortical motions. Particle image velocimetry measurements of the streamwise and wall-normal velocity components are correlated with a vortex marker (swirling strength) in the streamwise–wall-normal plane, and linear stochastic estimation is used to estimate the conditional average of the two-dimensional velocity field associated with a swirling motion. The mean structure consists of a series of swirling motions located along a line inclined at 12°–13° from the wall. The pattern is consistent with the observations of outer-layer wall turbulence in which groups of hairpin vortices occur aligned in the streamwise direction. While the observational evidence for the aforementioned model was based upon both experimental and computational visualization of instantaneous structures, the present results show that, on average, the instantaneous structures occur with sufficient frequency, strength, and order to leave an imprint on the statistics of the flow as well. Results at Reτ = 547 and 1734 are presented.

Simulations of MHD Turbulence in a Strongly Magnetized Medium

Abstract: We analyze 3D numerical simulations of driven incompressible magnetohydrodynamic (MHD) turbulence in a periodic box threaded by a moderately strong external magnetic field. We sum over nonlinear interactions within Fourier wavebands and find that the time scale for the energy cascade is consistent with the Goldreich-Sridhar model of strong MHD turbulence. Using higher order longitudinal structure functions we show that the turbulent motions in the plane perpendicular to the local mean magnetic field are similar to ordinary hydrodynamic turbulence while motions parallel to the field are consistent with a scaling correction which arises from the eddy anisotropy. We present the structure tensor describing velocity statistics of Alfvenic and pseudo-Alfvenic turbulence. Finally, we confirm that an imbalance of energy moving up and down magnetic field lines leads to a slow decay of turbulent motions and speculate that this imbalance is common in the interstellar medium where injection of energy is intermittent both in time and space.

Navier-Stokes Equations and Turbulence by C. Foias

Abstract: A catalog record for this book is available from the British Library.

The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence

Abstract: The variational multiscale method is applied to the large eddy simulation (LES) of homogeneous, isotropic flows and compared with the classical Smagorinsky model, the dynamic Smagorinsky model, and direct numerical simulation (DNS) data. Overall, the multiscale method is in better agreement with the DNS data than both the Smagorinsky model and the dynamic Smagorinsky model. The results are somewhat remarkable when one realizes that the multiscale method is almost identical to the Smagorinsky model (the least accurate model!) except for removal of the eddy viscosity from a very small percentage of the lowest modes.

Compressible Magnetohydrodynamic Turbulence in Interstellar Plasmas

Abstract: Radio wave scintillation observations reveal a nearly Kolmogorov spectrum of density fluctuations in the ionized interstellar medium. Although this density spectrum is suggestive of turbulence, no theory relevant to its interpretation exists. We calculate the density spectrum in turbulent magnetized plasmas by extending the theory of incompressible magnetohydrodynamic (MHD) turbulence given by Goldreich & Sridhar to include the effects of compressibility and particle transport. Our most important results are as follows: 1. Density fluctuations are due to the slow mode and the entropy mode. Both modes are passively mixed by the cascade of shear Alfven waves. Since the shear Alfven waves have a Kolmogorov spectrum, so do the density fluctuations. 2. Observed density fluctuation amplitudes constrain the nature of MHD turbulence in the interstellar medium. Slow mode density fluctuations are suppressed when the magnetic pressure is less than the gas pressure. Entropy mode density fluctuations are suppressed by cooling when the cascade timescale is longer than the cooling timescale. These constraints imply either that the magnetic and gas pressures are comparable or that the outer scale of the turbulence is very small. 3. A high degree of ionization is required for the cascade to survive damping by neutrals and thereby to extend to small length scales. Regions that are insufficiently ionized produce density fluctuations only on length scales larger than the neutral damping scale. These regions may account for the excess of power that is found on large scales. 4. Provided that the thermal pressure exceeds the magnetic pressure, both the entropy mode and the slow mode are damped on length scales below that at which protons can diffuse across an eddy during the eddy's turnover time. Consequently, eddies whose extents along the magnetic field are smaller than the proton collisional mean free path do not contribute to the density spectrum. However, in MHD turbulence eddies are highly elongated along the magnetic field. From an observational perspective, the relevant length scale is that transverse to the magnetic field. Thus, the cutoff length scale for density fluctuations is significantly smaller than the proton mean free path. 5. The Alfven mode is critically damped at the transverse length scale of the proton gyroradius and thus cascades to smaller length scales than either the slow mode or the entropy mode.

On the breakdown of boundary layer streaks

Abstract: A scenario of transition to turbulence likely to occur during the development of natural disturbances in a flat-plate boundary layer is studied. The perturbations at the leading edge of the flat plate that show the highest potential for transient energy amplication consist of streamwise aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with signicant spanwise modulation. Direct numerical simulations are used to follow the nonlinear evolution of these streaks and to verify secondary instability calculations. The theory is based on a linear Floquet expansion and focuses on the temporal, inviscid instability of these flow structures. The procedure requires integration in the complex plane, in the coordinate direction normal to the wall, to properly identify neutral modes belonging to the discrete spectrum. The streak critical amplitude, beyond which streamwise travelling waves are excited, is about 26% of the free-stream velocity. The sinuous instability mode (either the fundamental or the subharmonic, depending on the streak amplitude) represents the most dangerous disturbance. Varicose waves are more stable, and are characterized by a critical amplitude of about 37%. Stability calculations of streamwise streaks employing the shape assumption, carried out in a parallel investigation, are compared to the results obtained here using the nonlinearly modied mean elds; the need to consider a base flow which includes mean flow modication and harmonics of the fundamental streak is clearly demonstrated.

Mean Flow and Turbulence Structure of Open-Channel Flow through Non-Emergent Vegetation

Abstract: The ability of turbulence models, based on two equation closure schemes (the k-e and the k-ω formulations) to compute the mean flow and turbulence structure in open channels with rigid, nonemergent vegetation is analyzed. The procedure, developed by Raupach and Shaw (1982), for atmospheric flows over plant canopies is used to transform the 3D problem into a more tractable 1D framework by averaging the conservation laws over space and time. With this methodology, form/drag related terms arise as a consequence of the averaging procedure, and do not need to be introduced artificially in the governing equations. This approach resolves the apparent ambiguity in previously reported values of the drag-related weighting coefficients in the equations for the turbulent kinetic energy and dissipation rates. The working hypothesis for the numerical models is that the flux gradient approximation applies to spatial/temporal averaged conservation laws, so that the eddy viscosity concept can be used. Numerical results ar...

Compressible MHD Turbulence in Interstellar Plasmas

Abstract: Radio-wave scintillation observations reveal a nearly Kolmogorov spectrum of density fluctuations in the ionized interstellar medium. Although this density spectrum is suggestive of turbulence, no theory relevant to its interpretation exists. We calculate the density spectrum in turbulent magnetized plasmas by extending the theory of incompressible MHD turbulence given by Goldreich & Sridhar to include the effects of compressibility and particle transport. Our most important results are as follows. (1) Density fluctuations are due to the slow mode and the entropy mode. Both modes are passively mixed by the cascade of shear Alfven waves. Since the shear Alfven waves have a Kolmogorov spectrum, so do the density fluctuations. (2) Observed density fluctuation amplitudes imply either that the magnetic and gas pressures are comparable, or that the outer scale of the turbulence is very small. (3) A high degree of ionization is required for the cascade to survive damping by neutrals and thereby to extend to small lengthscales. Regions that are insufficiently ionized produce density fluctuations only on lengthscales larger than the neutral damping scale. These regions may account for the excess of power that is found on large scales. (4) Both the entropy mode and the slow mode are damped on lengthscales below that at which protons can diffuse across an eddy during the eddy's turnover time. Consequently, eddies whose extents along the magnetic field are smaller than the proton collisional mean free path do not contribute to the density spectrum. However, in MHD turbulence eddies are highly elongated along the magnetic field. From an observational perspective, the relevant lengthscale is that transverse to the magnetic field. Thus the cut-off lengthscale for density fluctuations is significantly smaller than the proton mean free path.

The Efficiency of Mixing in Turbulent Patches: Inferences from Direct Simulations and Microstructure Observations

Abstract: The time evolution of mixing in turbulent overturns is investigated using a combination of direct numerical simulations (DNS) and microstructure profiles obtained during two field experiments. The focus is on the flux coefficient G, the ratio of the turbulent buoyancy flux to the turbulent kinetic energy dissipation rate e .I n observational oceanography, a constant value G5 0.2 is often used to infer the buoyancy flux and the turbulent diffusivity from measured e. In the simulations, the value of G changes by more than an order of magnitude over the life of a turbulent overturn, suggesting that the use of a constant value for G is an oversimplification. To account for the time dependence of G in the interpretation of ocean turbulence data, a way to assess the evolutionary stage at which a given turbulent event was sampled is required. The ratio of the Ozmidov scale LO to the Thorpe scale LT is found to increase monotonically with time in the simulated flows, and therefore may provide the needed time indicator. From the DNS results, a simple parameterization of G in terms of LO/ LT is found. Applied to observational data, this parameterization leads to a 50%‐60% increase in median estimates of turbulent diffusivity, suggesting a potential reassessment of turbulent diffusivity in weakly and intermittently turbulent regimes such as the ocean interior.

Large-eddy simulation of turbulent gas–particle flow in a vertical channel: effect of considering inter-particle collisions

Abstract: The interaction between a turbulent gas flow and particle motion was investigated by numerical simulations of gas–particle turbulent downward flow in a vertical channel. In particular the effect of inter-particle collision on the two-phase flow field was investigated. The gas flow field was obtained by large-eddy simulation (LES). Particles were treated by a Lagrangian method, with inter-particle collisions calculated by a deterministic method. The spatial resolution for LES of gas–solid two-phase turbulent flow was examined and relations between grid resolution and Stokes number are presented. Profiles of particle mean velocity, particle wall-normal fluctuation velocity and number density are flattened as a result of inter-particle collisions and these results are in good agreement with experimental measurements. Calculated turbulence attenuation by particles agrees well with experimental measurements for small Stokes numbers, but not for large Stokes number particle. The shape and scale of particle concentrations calculated considering inter-particle collision are in good agreement with experimental observations.

Exact coherent structures in channel flow

Abstract: Exact coherent states in no-slip plane Poiseuille flow are calculated by homotopy from free-slip to no-slip boundary conditions. These coherent states are unstable travelling waves. They consist of wavy low-speed streaks flanked by staggered streamwise vortices closely resembling the asymmetric coherent structures observed in the near-wall region of turbulent flows. The travelling waves arise from a saddle-node bifurcation at a sub-turbulent Reynolds number with wall-normal, spanwise and streamwise dimensions smaller than but comparable to 50 + , 100 + and 250 + , respectively. These coherent solutions come in pairs with distinct structure and instabilities. There is a three-dimensional continuum of such exact coherent states

Intermittent distribution of inertial particles in turbulent flows.

Abstract: We consider inertial particles suspended in an incompressible turbulent flow. Because of particles' inertia their flow is compressible, which leads to fluctuations of concentration significant for heavy particles. We show that the statistics of these fluctuations is independent of details of the velocity statistics, which allows us to predict that the particles cluster on the viscous scale of turbulence and describe the probability distribution of concentration fluctuations. We discuss the possible role of the clustering in the physics of atmospheric aerosols, in particular, in cloud formation.